Scilab function
Last update : September 1995

circuit - finds a circuit or the rank function in a directed graph

### Calling Sequence

  `[p,r] = circuit(g)`

### Parameters

- `g`: graph list
- `p`: row vector of integer numbers of the arcs of the circuit if it exists
- `r`: row vector of rank function if there is no circuit

### Description

`circuit` tries to find a circuit for the directed graph `g`. It returns the circuit `p` as a row vector of the corresponding arc numbers if it exists and it returns the empty vector `[]` otherwise. If the graph has no circuit, the rank function is returned in `r`, otherwise its value is the empty vector `[]`.

### Examples

    // graph with circuit
    ta=[1 1 2 3 5 4 6 7 7 3 3 8 8 5];
    he=[2 3 5 4 6 6 7 4 3 2 8 1 7 4];
    g=make_graph('foo',1,8,ta,he);
    g('node_x')=[116 231 192 323 354 454 305 155];
    g('node_y')=[ 118 116 212 219 117 185 334 316];
    show_graph(g);
    p=circuit(g)
    show_arcs(p)
    // graph without circuit
    g=make_graph('foo',1,4,[1 2 2 3],[2 3 4 4]);
    [p,r]=circuit(g)